Claude Aime

Stellar coronagraphy with prolate apodized circular apertures

This paper generalizes to circular apertures the theoretical study of stellar coronagraphy with prolate apodized rectangular entrance apertures of Aime et al. (2002). The main difference between the two studies is that circular prolate spheroidal functions are used for a circular aperture instead of linear prolate spheroidal functions for rectangular apertures. Owing to the radial property of the problem, the solution to the general equation for coronagraphy is solved using a Hankel transform instead of a product of Fourier transforms in the rectangular case. This new theoretical study permits a better understanding of coronagraphy, stressing the importance of entrance pupil apodization. A comparison with the classical unapodized Lyot technique is performed: a typical gain of 10 4 to 10 6 can be obtained theoretically with this technique. Circular and rectangular apertures give overall comparable results: a total extinction of the star light is obtained for Roddier & Roddiers phase mask technique whilst optimal starlight rejections are obtained with a Lyot opaque mask. A precise comparison between a circular aperture and a square aperture of same surface favors the use of a circular aperture for detection of extrasolar planets.

Total coronagraphic extinction of rectangular apertures using linear prolate apodizations

This paper presents a theoretical study of stellar coronagraphy with apodized entrance apertures. The study is restricted to a perfect telescope operating in space, and a monochromatic on-axis unresolved star. It is shown that linear prolate functions are the optimal apodizers for rectangular apertures in stellar coronagraphy. With the phase mask technique (Roddier & Roddier 1997), prolate functions can produce a total extinction of the star light. For Lyots coronagraphy, the extinction is not complete, but prolate apodizations lead to an optimal star residual intensity with surprising interesting properties: the residual star light and the planet enjoy the same apodized intensity pattern (but dierent dynamic) with the optimal light concentration. With this technique, very high rejection rates can be obtained for Lyots coronagraphy, with smaller mask sizes.

A general method to devise maximum-likelihood signal restoration multiplicative algorithms with non-negativity constraints

Abstract The aim of the present paper is to give a general method allowing us to devise maximum-likelihood multiplicative algorithms for inverse problems, and particularly for signal and image restoration with non-negativity constraint. We consider the case of a Gaussian additive noise and that of a Poisson process. The method is founded on the Kuhn–Tucker first-order optimality conditions and the algorithms are developed to satisfy these conditions. The proposed method can be used for any convex function whose definition range includes the domain of constraints. It allows to obtain generalized forms of classical algorithms (ISRA and RLA) and to unify the method for obtaining these algorithms. We give relaxed forms of the algorithms to increase the convergence speed; moreover, the effect of the constraints is clearly shown. For a better understanding of the method to take into account the constraints, we express the non-negativity constraint using different functions and we reach a large class of algorithms that can be analyzed as descent algorithms. Then, we can justify and analyze the behavior of several algorithms suggested in the literature. The particular displacement directions appearing in such algorithms are evidenced and the convergence speed is analyzed. The algorithms are applied for simulated data, to a two-dimensional deconvolution problem, to show their performance and effectiveness. A support constraint is taken into account implicitly in the algorithms. Our method can be extended to more general hard constraints on the extreme values or on the support of the solution and a regularization of the problem can be easily introduced in the method.

Speckle Noise and Dynamic Range in Coronagraphic Images

This paper is concerned with the theoretical properties of high-contrast coronagraphic images in the context of exoplanet searches. We derive and analyze the statistical properties of the residual starlight in coronagraphic images and describe the effect of a coronagraph on the speckle and photon noise. Current observations with coronagraphic instruments have shown that the main limitations to high-contrast imaging are due to residual quasi-static speckles. We tackle this problem in this paper and propose a generalization of our statistical model to include the description of static, quasi-static, and fast residual atmospheric speckles. The results provide insight into the effects on the dynamic range of wave front control, coronagraphy, active speckle reduction, and differential speckle calibration. The study is focused on ground-based imaging with extreme adaptive optics, but the approach is general enough to be applicable to space, with different parameters.

THE USEFULNESS AND LIMITS OF CORONAGRAPHY IN THE PRESENCE OF PINNED SPECKLES

In this Letter we study the utility and limitations of ground-based coronagraphy with adaptive optics (AO). In very high AO correction regimes, residual speckles are pinned on the diffraction rings of the Airy pattern. We show that this effect is due to small errors in the complex wave in the focal plane, amplified by the coherent part of the wave. The statistics of these speckles are fairly well described by a modified Rician distribution. The variance of the speckles, at high flux and at photon-counting levels, finds simple expressions. The total variance can be partitioned into two contributions: one that can be suppressed by a coronagraph and one that cannot. Different regimes can be identified. These results enable us to analyze when a coronagraph can defeat the noise variance, and they provide a criterion for the effectiveness of such instruments.

Achromatic dual-zone phase mask stellar coronagraph

This paper presents a generalization of the Roddier & Roddier Phase Mask coronagraph for polychromatic obser- vations. It is shown that using a dual-zone phase mask, combined with complex apodization, both phase and size chromatism can be compensated simultaneously to produce high extinction of a point source over large bandwidths, for example the entire K band with a residual integrated starlight of 3.2 × 10 −4 and a star intensity level of 10 −6 at an angular separation of 3λ/D. Other advantages of the proposed technique include the compatibility with centrally obscured telescopes, absence of blind axes and no symmetrization of the images.

APODIZED PUPIL LYOT CORONAGRAPHS FOR ARBITRARY APERTURES. II. THEORETICAL PROPERTIES AND APPLICATION TO EXTREMELY LARGE TELESCOPES

We study the application of Lyot coronagraphy to future Extremely Large Telescopes (ELTs), showing that Apodized Pupil Lyot Coronagraphs enable high-contrast imaging for exoplanet detection and characterization with ELTs. We discuss the properties of the optimal pupil apodizers for this application (generalized prolate spheroidal functions). The case of a circular aperture telescope with a central obstruction is considered in detail, and we discuss the effects of primary mirror segmentation and secondary mirror support structures as a function of the occulting mask size. In most cases where inner working distance is critical, e.g., for exoplanet detection, these additional features do not alter the solutions derived with just the central obstruction, although certain applications such as quasar-host galaxy coronagraphic observations could benefit from designs that explicitly accomodate ELT spider geometries. We illustrate coronagraphic designs for several ELT geometries including ESO/OWL, the Thirty Mirror Telescope, the Giant Magellan Telescope, and describe numerical methods for generating these designs.

Radon approach to shaped and apodized apertures for imaging exoplanets

In this paper, we present a new approach to the study of shaped and apodized apertures for the detection of exoplanets. It is based on a Radon transform of the telescope aperture and makes it possible to present the effects of shaped and apodized apertures in a unified manner for an objective comparison between them. An illustration of this approach is made for a few apertures. Our conclusion favors the apodized apertures. The approach also permits us to obtain new results. In a second part of the paper, we derive expressions for the signal-to-noise ratio (SNR) of an experiment using an apodized aperture and draw the corresponding curves for the example of a circular telescope apodized by a prolate spheroidal function. We found that a very marked improvement of the SNR can be obtained using apodization techniques. There is an apodization that optimizes the SNR for a given observation; this apodization is generally very strong. The analysis is made for the case of a perfect telescope operated in space.

Interferometric apodization of rectangular apertures - Application to stellar coronagraphy

We describe the principle of an apodization technique for rectangular apertures that can be implemented using a Michelson or a Mach-Zender interferometer. Using several interferometers, any integer power of cosine functions can be obtained. The technique is considered for application to the Apodized Square Aperture (ASA) concept recently proposed by Nisenson & Papaliolios (2001). Simple analytic expressions for the Point Spread Functions of such apodized apertures are given. For a cosine to the power N apodization, the resulting focal plane amplitude is simply the sum of N + 1 weighted and shifted sine cardinal functions. The interest of such apodized apertures for coronagraphy is investigated. It appears that these apodization functions are very ecient provided that only a central part of the cosine-arch is used. Analytic expressions are derived for the residual amplitude left in an image of the aperture after the coronagraphic experiment. Best results are obtained with a cosine squared apodization.

Contribution to the space-time study of stellar speckle patterns

The temporal behavior of stellar speckle patterns is statistically analyzed. The time-only power spectrum is shown to be the sum of two exponentially decreasing functions defining two characteristic time constants. The corresponding correlation is the sum of two Lorentzian functions. This is consistent with the first-order expansion of the power spectrum deduced from the multiple-layer model for atmospheric turbulence. However, this model fails to account for the experimental data that show a strong correlation between the spatial structure of a speckle pattern and its temporal behavior. This leads to the introduction of a new empirical model, called the randomly jittered speckle pattern model, which gives a preponderant place to image motion. The speckle lifetime then appears to be substantially longer than the corresponding measured time constant. As a consequence, a preliminary compensation of the image motion appears to be particularly interesting in speckle interferometry or active optics experiments.